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LUCKY_DIMON [66]
2 years ago
8

A boy standing on the shore of a lake 1 mile wide wants to reach the fast-food restaurant 3 miles down the shore on the opposite

side of the lake. If he swims at 2 mph and walks at 4 mph, is it quicker for him to swim directly across the lake and walk to the restaurant or to swim directly to the restaurant? How much quicker? Explain.
Mathematics
1 answer:
evablogger [386]2 years ago
5 0

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bit.^{}ly/3a8Nt8n

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How do u set up the word problem
galina1969 [7]

Answer:

8 feet

Step-by-step explanation:

First, draw a picture.  The pole is 22 feet tall.  Katherine is 5.5 feet tall.  She is 24 feet from the pole.  The light from the top of the pole to the tip of her shadow forms two similar right triangles.  The length of her shadow is x.

Now use similar triangles to write a proportion:

22 / (24 + x) = 5.5 / x

Cross multiply:

22x = 5.5 (24 + x)

Distribute:

22x = 132 + 5.5x

Combine like terms:

16.5x = 132

Divide:

x = 8

The shadow is 8 feet long.

6 0
3 years ago
A triangle with angle measures of 20° and 30° is a (FILL IN THE BLANK) triangle.
White raven [17]
Obtuse triangle, if the two angles add up to 50 degrees and a whole triangle equals 180 degrees. That means the third angle is greater than 90 degrees and only obtuse angles are greater than 90 degrees
7 0
2 years ago
PEF and triangle GHI are similar right triangles.
LekaFEV [45]

Answer: it’s the first 1

Step-by-step explanation:

6 0
2 years ago
Find the domain of the function
Svetradugi [14.3K]

Answer:

<em>The domain of f is (-∞,4)</em>

Step-by-step explanation:

<u>Domain of a Function</u>

The domain of a function f is the set of all the values that the input variable can take so the function exists.

We are given the function

f(x)=\frac{1}{\sqrt{4-x} }

It's a rational function which denominator cannot be 0. In the denominator, there is a square root whose radicand cannot be negative, that is, 4-x must be positive or zero, but the previous restriction takes out 0 from the domain, thus:

4 - x > 0

Subtracting 4:

- x > -4

Multiplying by -1 and swapping the inequality sign:

x < 4

Thus the domain of f is (-∞,4)

7 0
2 years ago
Simplify x+2/x^2+2x-3 divide by x+2/x^2-x
ira [324]

\dfrac{\frac{x+2}{x^2+2x-3}}{\frac{x+2}{x^2-x}}

If x\neq-2, then we can immediately cancel the factors of x+2:

\dfrac{\frac1{x^2+2x-3}}{\frac1{x^2-x}}=\dfrac{x^2-x}{x^2+2x-3}

Factorize the numerator and denominator:

x^2-x=x(x-1)

x^2+2x-3=(x+3)(x-1)

Next, if x\neq1, then

\dfrac{x^2-x}{x^2+2x-3}=\dfrac{x(x-1)}{(x+3)(x-1)}=\dfrac x{x+3}

8 0
3 years ago
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